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3 parts per billion Berlin Pond
microbial (bugs and stuff), inorganic (minerals), pesticides (kills bugs and stuff), herbicides (kills plants) radioactive, organic (dead stuff) Unit Typical Sources old pipes, old paint, sinkers, bullets, natural mineral deposits ppb 3 not given parts per billion parts of what? per billion what?... oh dear Next question Would you drink the water?
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so, next… we need to understand the numbers
Unit Typical Sources old pipes, old paint, sinkers, bullets, natural mineral deposits ppb 3 not given parts per billion parts of what? per billion what?... oh dear define percentile…. 90th percentile means that 90% of the samples tested had a level of lead at or below 3 ppb tells us that there were a number of measurements made AND that there is a range of results (not all the values are the same) so, next… we need to understand the numbers we need to know if they are right and we need to know how sure we are so how do we know which measurement is right? or if any are right? AND how sure can we be of that conclusion?
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the measured value is correct? (accurate)
Numbers in Science…. Accuracy, Precision (Significant Figures) two issues with numbers…. how do we know: if _______________________________________ and _________________________________________ the measured value is correct? (accurate) how certain are we of the value? (precision) (to what place can we report our measurement?) OR 4000
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whole numbers with respect to what we can count
Numbers in Science…. Accuracy, Precision (Significant Figures) Types of numbers (we’ll deal with two types…) Exact What does ‘exact’ mean? two types of exact numbers: _____________________________________ ex: whole numbers with respect to what we can count definitions (unit equalities) 100 centimeters = 1 meter centi means 1/100th 2.54 cm = 1 in (exactly) 1000 grams = 1 kilogram kilo means 1000 4.184 J = 1 cal (exactly) 1,000,000,000 nanoseconds = 1 sec nano means 1/1,000,000,000th
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whole numbers with respect to what we can count
Numbers in Science…. Accuracy, Precision (Significant Figures) Types of numbers (we’ll deal with two types…) Exact What does ‘exact’ mean? two types of exact numbers: _____________________________________ ex: whole numbers with respect to what we can count definitions (unit equalities) 100 centimeters = 1 meter centi means 1/100th 2.54 cm = 1 in (exactly) 1000 grams = 1 kilogram kilo means 1000 4.184 J = 1 cal (exactly) How do we know these are correct (accurate)? _________________________________ definitions are definitions have to trust we counted right
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Measured (the other type of number we’ll deal with)
start with __________________________ make a measurement….. a single measurement click on image for link
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Accuracy (correctness)
Number 1 – presume that you read the instructions, and you are using the measuring device correctly… Next… some data: volume graduated cylinder _____________ Erlenmeyer flask ______________ mass electronic (digital) balance __________ triple beam balance ____________ which do you think is right? why? grad cyl Erlen which do you think is right? why? elec (dig) tbb
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YOU DON’T WE DON’T TRUST
so,… you think “this” _____________ is more correct that “that” _______________ or,… you think “this” _______________ is more correct that “that” _______________ or,… you think “this” _______________ is more correct that “that” _______________ how do you know if either is right? _________________________________ so,… how can these instruments be useful if you are not sure which is right or if either is right? Erlenmeyer graduated cylinder graduated cylinder Erlenmeyer digital balance triple beam balance triple beam balance digital balance YOU DON’T the instruments need to have been manufactured according to some known standard defined, constant, reproducible you have to TRUST the manufacturer for the balances, we have a ______________________ how do we know it is 200 g? _______________________ we have to _______________________ 200 g standard WE DON’T TRUST
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calibrate the balances…. (or any measuring device)
use a standard to check for accuracy or adjust for accuracy calibration marks: the incremental marks made on an instrument based on using a standard
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we have to use the instrument correctly TRUST standard
Precision How sure are we?.... The Ruler and The Red Paper (precision on single measurements) How do we know the measured value is right? (________________) ____________________________________________ and have to _____________ the manufacturer made the instrument according to some _______________ How certain are we of the value? (_____________) accuracy we have to use the instrument correctly TRUST standard precision to what place can we record our answer and with what certainty
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THE RULER AND THE WIDTH OF THE RED PAPER
1 meter side calibration marks ____ marks at each ____ @ _______________ know > ____ m and < ____ m estimate > ____ m and < ____ m somewhere between ___ ___ m to ___ ___ m 2 m 0 m and 1 m (certain) 1 (b/c the edge of the paper is within these “bounds” (calibration marks)) (not so certain) (in this range) certain estimated (sure / positive) (speculated / less certain / some guessing) slide 14
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(speculated / less certain /
THE RULER AND THE WIDTH OF THE RED PAPER 1 decimeter (dm) side calibration marks ____ marks at each ____ @ _______________ know > ____ dm and < ____ dm estimate > ____ dm and < ____ dm somewhere between ___ ___ dm to ___ ___ dm 11 dm 0 dm, 1 dm … 10 dm (certain) 6 7 (not so certain) (in this range) certain estimated (sure / positive) slide 14 (speculated / less certain / some guessing)
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(speculated / less certain /
THE RULER AND THE WIDTH OF THE RED PAPER 1 centimeter (cm) side calibration marks ____ marks at each ____ @ _______________ know > ____ cm and < ____ cm estimate > ____ cm and < ____ cm somewhere between ___ ___ cm to ___ ___ cm 101 cm 0, 1, 2, … 100 cm (certain) 60 61 (not so certain) (in this range) certain estimated (sure / positive) slide 14 (speculated / less certain / some guessing)
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the digits we are certain of…. meter side
decimeter side centimeter side calibrated (marked) at meters, certain of ______________ calibrated (marked) at decimeters, certain of _____________ calibrated (marked) at centimeters, certain of _______________ meters’ place decimeters’ place centimeters’ place the digits we are estimating meter side decimeter side centimeter side calibrated (marked) at meters, estimate ______________ calibrated (marked) at decimeters, estimate _____________ calibrated (marked) at centimeters, estimate _______________ tenth of meters’ place tenth of dms’ place tenth of cms’ place the digits we are sure of correspond to ___________________________ the estimated digits correspond to _______________________________ the calibration marks between the calibration marks
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the estimated place depends on /determined by
the digits we are sure of correspond to ___________________________ the estimated digits correspond to _______________________________ can (and must to use the instrument correctly) ________________________________________ our rule: we will limit our estimation on a measurement to _______ estimated place the calibration marks between the calibration marks estimate between the calibration marks 1 mm (0.1 cm or m) ONE the estimated place depends on /determined by the calibration marks for the above ruler, can (and must) estimate to the __________________________ 0.1 mm (or 0.01 cm or m) place
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dry dry dry
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we are NOT going to do this!!
estimate the estimated digit might be ____________ or ______________ example: _____ __ cm a “little more” a “little less” certain estimated determines the range of possibilities centers on the most likely value to know what that “little more” or “little less” is a LOT (ideally an infinite #) of people need to make the measurement a LOT of times. The set of measurements would start to center on a value and the distribution would be a normal (bell-shaped) distribution. we are NOT going to do this!! The width of the distribution would be the “little more” or “little less”
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estimate the estimated digit might be ____________ or ______________ example: _____ __ cm a “little more” a “little less” certain estimated determines the range of possibilities the “littlest more” a digit can be is ______ the “littlest less” a digit can be is ______ so, for _____ __ cm, the estimated digit is in the ________________ the “littlest more” the estimated digit can be is ____ the “littlest less” the estimated digit can be is ____ + 1 - 1 tenths place + .1 - .1
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the “littlest more” a digit can be is ______
the “littlest less” a digit can be is ______ so, for _____ __ cm, the estimated digit is in the ________________ the “littlest more” the estimated digit can be is ____ the “littlest less” the estimated digit can be is ____ + 1 - 1 tenths place + .1 - .1 the smallest range of possible values reflecting the uncertainty in estimating ( _______ + _____ ) cm to ( ________ - ______ ) cm OR _________ cm to _________ cm ________ _______ cm 0.1 0.1 the range the minimum uncertainty on the measurement 0.1
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The minimum range on any measured value is _________________________
uncertainty The minimum range on any measured value is _________________________ we (MHS Chemistry) will use this __________________________ ___________________________________________ 1 in the estimated digit on single measured values unless told otherwise what is equally important to recognize is… EVERY time a measurement is made, the measured value has at least this uncertainty so, EVERY MEASURED VALUE HAS UNCERTAINTY there is no such thing as an exact measurement
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the uncertainty tells us the estimated digit
glass 80 mL 1 10 mL 1 meniscus tens place 70 mL 80 mL 70 water 1 mL this uncertainty applies any time you use the instrument calibrated to bottom of meniscus estimated 70 mL 1 mL 1 66 mL 67 mL 60 .1 mL estimated the uncertainty tells us the estimated digit tells us you can, and MUST, estimate to that place
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grams slider weight 0.1 g 1 to the best of your knowledge, the mass is
-1 0.1 g 1 to the best of your knowledge, the mass is between 3.4 g 3.5 g 0.01 g estimated tells us you can and MUST estimate to that place
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in notes, the pointer is at 5.6 (OOPS)
increments of ____ sci. not. ___ 10 ___ know > ______ and < ______ estimate ________ ( ________ ) increments of ____ sci. not. ___ 10 ___ know > ______ and < ______ estimate ________ ( ________ )
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in notes, the pointer is at 5.6 (OOPS)
increments of ____ sci. not. ___ 10 ___ know > ______ and < ______ estimate ________ ( ________ ) 0.1 g 1 -1 this uncertainty applies every time you use the instrument 0.01 g increments of ____ sci. not. ___ 10 ___ know > ______ and < ______ estimate ________ ( ________ ) 0.1 g 1 -1 0.01 g
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increments of ____ sci. not. ___ 10 ___
know > ______ and < ______ estimate ________ ( ________ )
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it’s right at 4! but it’s not… because there is no “right at 4”…
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the width of the yellow paper…
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The marks are called calibration marks.
Focusing on the 28 cm calibration mark. Since the mark itself has a width, it is not certain where 28 cm is. One could only be absolutely certain where 28 cm is, if the calibration mark was infinitely thin... but then you couldn’t see the calibration mark.
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it’s right at 4.5! but it’s not… because there is no “right at 4.5”… One could only be absolutely certain where 4.5 grams is, if the calibration mark was infinitely thin... and the pointer was infinitely thin… but then you couldn’t see the calibration mark or the pointer.
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because there is no “right at 4”…
One could only be absolutely certain where 4 grams is, if the calibration mark was infinitely thin... but then you couldn’t see the calibration mark. it’s right at 4! but it’s not…
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increments of ____ sci. not. ___ 10 ___
know > ______ and < ______ estimate ________ ( ________ ) 0.1 g 1 -1 this uncertainty applies every time you use the instrument 0.01 g
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dry dry dry hang in there
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increments of ____ sci. not. ___ 10 ___
know > ______ and < ______ estimate ________ ( ________ ) 50 mL 5 1 10 mL the first place you are estimating is the tens place increments of ____ sci. not. ___ 10 ___ know > ______ and < ______ estimate ________ ( ________ ) 0.2 mL 2 -1 0.1 mL the first place you are estimating is the tenths place
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increments of ____ sci. not. ___ 10 ___
know > ______ and < ______ estimate ________ ( ________ ) 25 mL 2.5 1 10 mL the first place you are estimating is the tens place
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FINAL RULES… precision
increments of ________ sci. not. ___ 10__ estimate ________ ( _______) When the increment can be written as 1 10something then _________________________________ _____________________________________ 10 mL 1 one in the tens place 1 1 mL uncertainty in ones place one in the ones place 1 mL 1 graduated cylinders .1 mL uncertainty in tenths place one in the tenths place .1 g 1 -1 triple beam balances .01 g uncertainty in hundredths place one in some place you can estimate to one more place than the calibration (increment)
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FINAL RULES… precision
beaker increments of ________ sci. not. ___ 10__ estimate ________ ( _______) When the increment is NOT 1 10something then _________________________________ _____________________________________ 50 mL 5 five in the tens place 1 10 mL uncertainty in tens place two in the tenths place .2 mL 2 -1 graduated cylinder .1 mL uncertainty in tenths place 25 mL 2.5 two.5 in the tens place 1 Erlenmeyer 10 mL uncertainty in tens place NOT one in some place you can estimate to the same place as the calibration (increment)
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